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intenzxboi
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Homework Statement
give the limit if it exist of (1-1/n)^n n=1 to infinity
the teacher wrote:
lim n goes to infinity (1+x/n)^n = e^x
so therefore
lim n goes to infinity (1-1/n)^n = e^-1
can someone explain this to me.
intenzxboi said:how I'm i suppose to know that
(1+x/n)^n = e^x ??
The limit of (1-1/n)^n is significant because it is a key concept in the study of calculus and the understanding of infinite processes. It helps us understand how a quantity can approach a specific value as its inputs approach infinity.
The limit of (1-1/n)^n is equal to the number e, which is approximately 2.71828. This means that as n approaches infinity, the value of (1-1/n)^n approaches e. In other words, e is the limit of (1-1/n)^n as n approaches infinity.
The formula for calculating e^-1 using the limit of (1-1/n)^n is 1/e, where e is the number defined as the limit of (1-1/n)^n as n approaches infinity.
e^-1, also known as the natural base, is an important number in mathematics and science because it is used to model many natural processes, such as growth and decay, and it appears in many mathematical equations and formulas. It is also commonly used in statistics, finance, and engineering.
The limit of (1-1/n)^n can be used in real-world applications to model continuous processes that involve growth or decay. For example, it can be used to calculate compound interest, population growth, and drug concentration in the body. Additionally, it is used in various fields of science, such as physics and biology, to describe natural phenomena.